Verbal and visual-spatial working memory and mathematical ability in different domains throughout primary school

Eva Van de Weijer-Bergsma 0 Evelyn H. Kroesbergen 0 Johannes E. H. Van Luit 0 0 E. Van de Weijer-Bergsma ( The relative importance of visual-spatial and verbal working memory for mathematics performance and learning seems to vary with age, the novelty of the material, and the specific math domain that is investigated. In this study, the relations between verbal and visual-spatial working memory and performance in four math domains (i.e., addition, subtraction, multiplication, and division) at different ages during primary school are investigated. Children (N = 4337) from grades 2 through 6 participated. Visual-spatial and verbal working memory were assessed using online computerized tasks. Math performance was assessed at the start, middle, and end of the school year using a speeded arithmetic test. Multilevel Multigroup Latent Growth Modeling was used to model individual differences in level and growth in math performance, and examine the predictive value of working memory per grade, while controlling for effects of classroom membership. The results showed that as grade level progressed, the predictive value of visual-spatial working memory for individual differences in level of mathematics performance waned, while the predictive value of verbal working memory increased. Working memory did not predict individual differences between children in their rate of performance growth throughout the school year. These findings are discussed in relation to three, not mutually exclusive, explanations for such age-related findings. - To solve a math problem, such as 7 12, a child needs to hold the relevant information in mind and manipulate this information. For example, this problem may be solved by the strategy to split this problem into subproblems (e.g., 7 10, 7 2 is 70 + 14), requiring the child to keep the answer to one of the subproblems in mind, while solving the second one, and adding the outcomes to produce the answer to the original problem. In addition or subtraction calculations with multiple digits, such as 27 + 59 or 47 19, carrying or borrowing of a digit from one column to another also requires a child to keep track of the manipulations and intermediate solutions. Indeed, there is ample of evidence that children with a higher working memory capacity have an advantage in mathematics (Frisovan den Bos, Van der Ven, Kroesbergen, & Van Luit, 2013; Raghubar, Barnes, & Hecht, 2010). The most widely used model of working memory (WM) includes several components: the central executive, phonological loop, visual-spatial sketchpad, and episodic buffer (Baddeley, 1986, 2000). The central executive is a domaingeneral, attentional control system involved in several processes such as the selection and execution of strategies, retrieval of information from long term memory, monitoring of input, simultaneously storing and processing of information, and the coordination of the other components of the WM system. The visual-spatial sketchpad involves temporary storage and rehearsal of visual and spatial information, while the phonological loop involves storage and rehearsal of phonological and auditory information. The episodic buffer a temporary storage system that is responsible for the integration of information from a variety of sources is the third slave system (Baddeley, 2000). Functioning of the two domain-specific slave systems is usually measured using simple span tasks, in which increasingly longer strings of information are immediately recalled without further processing. Functioning of the central executive is traditionally measured with complex span tasks, in which storage as well as processing or manipulation of information is required (Kail & Hall, 2001). In other words, working memory can be distinguished from short-term memory, which only involves the temporary storage of information by the slave systems, whereas working memory involves storage as well as processing of information. Although the central executive is a domaingeneral component, the tasks used to measure its functioning also tap into one (or both) of the domain-specific slave storage systems. The multicomponent nature of this model allows researchers to examine whether the use of different subcomponents in mathematics vary as a function of the type of math test, age, individual differences in ability level, and the type of strategy used (Raghubar et al., 2010). The central executive, as well as the visual-spatial sketchpad and the phonological loop have been shown to be associated with mathematics performance and learning in children (Alloway & Alloway, 2010; Bull, Espy, & Wiebe, 2008; De Smedt et al., 2009; Friso-van den Bos et al., 2013; Geary, 2011; Geary, Hoard, Byrd-Craven, & Catherine DeSoto, 2 004; Ho lme s & Adams, 2006 ; Imbo & Vandierendonck, 2007; Meyer, Salimpoor, Wu, Geary, & Menon, 2010; Raghubar et al., 2010; Swanson & BeebeFrankenberger, 2004; Swanson, 2006; Toll, Van der Ven, Kroesbergen, & Van Luit, 2011; Van der Ven, Van der Maas, Straatemeier, & Jansen, 2013). However, the strength of the relationship between different working memory modalities and mathematics performance is found to vary as a result of the type of mathematics tests used, and the strategies and mental models these tests elicit. In their recent meta-analysis, Friso-van den Bos and colleagues (2013) found the majority of working memory components to be more strongly associated with general mathematics tests, such as a national curriculum test and composite measures, than with purely arithmetical measures. General mathematics tests often include a broad variety of problem types, requiring children to switch between operations, strategies, and mental models. Nevertheless, even solving basic arithmetic problems may elicit both visualspatial and verbal representations and strategies (Imbo & LeFevre, 2010; Logie, Gilhooly, & Wynn, 1994). So, since solving mathematical problems may elicit visual-spatial as well as verbal representations and strategies, both visualspatial and verbal working memory components are likely to be involved in learning mathematics. Several studies indicate that the relationship between working memory and mathematics changes with age (Andersson & Lyxell, 2007; De Smedt et al., 2009; Henry & MacLean, 2003; Holmes & Adams, 2006; Kyttl, Aunio, & Hautamki, 2010; McKenzie, Bull, & Gray, 2003; Rasmussen & Bisanz, 2005; Van der Ven et al., 2013). The results from studies during preschool, primary school, and adolescence suggest that younger children rely more on visual-spatial working memory when learning and applying new mathematical skills, whereas older children rely more on verbal working memory after skills have been learned. Van der Ven et al. (2013) introduced three, not mutually exclusive, explanations for the decrease in the relationship between visual-spatial working memory and math performance as children grow older. First, according to the developmental explanation, younger children (...truncated)